Why does the page not reload when I save?

Because it does not need to. The plugin sends the form, gets the answer, and updates the screen where you are standing — the same handler runs on the server and the same checks are made, but you are not sent back to the top of a freshly-rendered page to find out whether it worked.

If anything goes wrong with that, the browser falls back to submitting the form the ordinary way, so nothing is ever stuck.